We became interested in this question and its connection to isomonodromy while
trying to understand [1]}. In that paper Biswas, Heu, and
Hurtubise raise question:bhh, asking whether it is possible to isomonodromically deform irreducible flat vector bundles to achieve semistability, by analogy to Hilbert's 21st problem (also known as the Riemann-Hilbert problem).
